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Your other problems seem to be related to some kind of electrical or transmission issue.
Parasitic power draw is very difficult to diagnose, I would recommend unplugging any accessory in the car, including the flashlight in the glove box.
The uneven idle, weird gear shifting, bad fuel economy, etc. all could be explained by a few different issues. If not the engine, I might suspect a transmission issue.
Engine:
Check the MAF sensor, spark plugs, and O2 sensors. Any of these failing would quickly rob power and cause further issues. The other possibility is a timing chain, which would be catastrophic if failed.
Intake:
Unlikely to be a problem unless the throttle body and turbocharger are mechanically broken. There would be many signs if these were the case
Transmission:
Could be shifting poorly due to bad adaptations or a lack of proper service. BMW's "lifetime" transmission fluid claim is widely disputed, if between 50-100k miles (80-160k kilometers) have a flush done
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